t^2+3st-4s^2=0

Solution for t^2+3st-4s^2=0 equation:

Simplifying
t2 + 3st + -4s2 = 0

Reorder the terms:
3st + -4s2 + t2 = 0

Solving
3st + -4s2 + t2 = 0

Solving for variable 's'.

Factor a trinomial.
(-4s + -1t)(s + -1t) = 0

Subproblem 1
Set the factor '(-4s + -1t)' equal to zero and attempt to solve:

Simplifying
-4s + -1t = 0

Solving
-4s + -1t = 0

Move all terms containing s to the left, all other terms to the right.

Add 't' to each side of the equation.
-4s + -1t + t = 0 + t

Combine like terms: -1t + t = 0
-4s + 0 = 0 + t
-4s = 0 + t
Remove the zero:
-4s = t

Divide each side by '-4'.
s = -0.25t

Simplifying
s = -0.25t
Subproblem 2
Set the factor '(s + -1t)' equal to zero and attempt to solve:

Simplifying
s + -1t = 0

Solving
s + -1t = 0

Move all terms containing s to the left, all other terms to the right.

Add 't' to each side of the equation.
s + -1t + t = 0 + t

Combine like terms: -1t + t = 0
s + 0 = 0 + t
s = 0 + t
Remove the zero:
s = t

Simplifying
s = t
Solution
s = {-0.25t, t}